Censored survival data occur when the exact survival time is known only for some individuals in a study, whereas for the rest of the individuals, it is only known that they were still alive at some time. The presence of censoring has consequences for how descriptive and inferential statistics should be performed. 

Statistics methods for the analysis of event history data has been a major research topic for the Section of Biostatistics since it was established in 1978. Members of the section have been influential in the development of the mathematical statistical properties and applications of methods in event history analysis. Aside from the numerous manuscripts on the topic, part of the work in this area has been summarized in the book Statistical Models Based on Counting Processes, published in 1993 by PK Andersen, Ø Borgan, RD Gill, and N Keiding. Further developments have been published in the book Dynamic Regression Models for Survival Data, published in 2006 by T Martinussen and TH Scheike.

Our faculty have developed or contributed to statistical software for event history analysis that is used by people all over the world. Some of the R packages developed at our section include:  mets, prodlim, eventglm, riskRegression, and timereg. 

Faculty working in this area

PK Andersen, PF Blanche, F Eriksson, TA Gerds, T Martinussen, B Ozenne, H Rytgaard, T Scheike

The field of causal inference deals with the challenges of inferring cause and effect (for example the effect of a new treatment or intervention) from data. This includes defining formal mathematical frameworks for causation, creating methods for inferring causal structures using data, developing efficient estimators for causal effects, and deriving bounds or sensitivity analyses for causal effects that are robust to certain assumptions. 

Our faculty have developed or contributed to statistical software for causal inference that is used widely. Some of the R packages developed at our section include: causaloptim, causalDisco, and pseval

Faculty working in this area

EE Gabriel, TA Gerds, A Jensen, T Martinussen, AH Petersen, H Rytgaard, MC Sachs 

Statistical accuracy measures such as Receiver Operating Characteristics (ROC) and utility functions like the Brier score are important tools for developing diagnostic and predictive models. The Section is frequently involved in applied projects where the aim is to predict the current status (diagnosis) or the future status (prediction) of new patients based on data. The Section is actively involved in the development of theory, methods, and computational tools for medical decision theory, including machine learning. Part of this work has been published in the book Medical Risk Prediction Models With Ties to Machine Learning by TA Gerds, M Kattan.

Our faculty have developed or contributed to statistical software for prediction modeling in the statistical software R. Some of the R packages developed at our Section include: plotROC, timeROC, wally, and riskRegression.

Faculty working in this area

PF Blanche, EE Gabriel, TA Gerds, J Hilden, MC Sachs

Statistical genetics is a multidisciplinary field that aims to understand the genetic basis of traits and diseases. Faculty in the Section play a vital role in developing statistical methods, analyzing genetic data, estimating heritability, investigating gene-environment interactions, and collaborating with other researchers to interpret the findings. Their contributions help advance our understanding of genetic influences on human health and complex traits. The methods and tools developed are applicable beyond genetics to all sorts of modern, high-dimensional -omics data.

Faculty working in this area

CT Ekstrøm, AK Jensen, A Meddis, T Scheike

Randomized controlled trials (RCTs) are powerful research designs used to evaluate the effectiveness and impact of interventions or treatments in medicine and public health. They are considered the gold standard for establishing causal relationships between an intervention and its outcomes. Faculty and staff at the Section play a critical role throughout the entire RCT process, from study design to data analysis and interpretation. Their expertise helps ensure the rigor, reliability, and validity of the trial, providing valuable evidence to inform decision-making and improve the quality of interventions in various medical research areas. They also develop theory and methods to improve the efficiency and reliability of RCTs.

Faculty working in this area

P Blanche, EE Gabriel, AKG Jensen, AK Jensen

Latent variable models are useful for analyzing multivariate response data. An important example is repeated measurements for the same variable at different time points. Such data can be analyzed in so-called mixed models, where latent variables are used to model the correlation in measurement for the same subject. The section has a strong expertise in these models and has developed the R package LMMstar for the application of such models.

Latent variable models are also used when observed data have measurement error. Here so-called measurement models are used to relate a multivariate observed variable to underlying latent variables (e.g. human intelligence). Statistical methods for the theory of response and measurement has a long history in Denmark. George Rasch (1901 - 1980) was a Danish mathematician and statistician who developed the Rasch model. Members of the Section have studied that and related models for many years (see e.g Rasch Models in Health, published in 2012 and edited by KB Christensen, S Kreiner, and M Mesbah). 

General latent variable models tries to causally relate latent variables to each other. This can be done in e.g. in Structural Equation Models which are DAG-models including latent variables. These models are useful e.g. for allowing for measurement errors in predictor variables and for dimension reduction. The Section is involved in the development of inference methods for such models and has created the lava R package for the use for general latent variable models. Furthermore, the standalone statistical software package DIGRAM for discrete graphical models was developed at the Section. 

Faculty working in this area

KB Christensen, E Budtz-Jørgensen, S Kreiner, JH Petersen, J Forman, B Ozenne, LT Skovgaard

Causal discovery is a field within statistics and machine learning focused on identifying cause-and-effect relationships from empirical data. Unlike traditional statistical methods that rely on prior knowledge or information about the system to be modelled, causal discovery leverages various algorithms and statistical techniques to recover parts of the data generating mechanism and infer causal structures. The results can be used for exploratory purposes, revealing new hypotheses about e.g. mechanisms responsible for a disease, or they can be used to obtain more accurate predictions and informed decision-making in diverse fields such as healthcare, economics, and social sciences. The Section is actively involved in the development of theory, methods, and computational tools for causal discovery in particular where temporal data are available to guide the the discoveries.

Our faculty have developed and contributed to statistical software for causal discovery, in particular the R package causalDisco

Faculty working in this area

AH Petersen, CT Ekstrøm

2023

• Anders Munch, Targeted learning with right-censored data
• Ann-Sophie Buchardt. Statistical analysis of genetic data: Interactions and multivariate outcome.
• Julie Kjærulff Furberg. Treatment effect measures for recurrent event endpoints with and without presence of terminal events.
• Jeppe Ekstrand Halkjær Madsen, Innovative statistical methods for assessing post approval drug safety based on real world user data.

2022

• Anne Helby Petersen. Data-driven causal model building for epidemiology. Can be obtained by request.

2021

• Asbjørn Thomas Maltesen. Analysis of multiple domains in longitudinal epidemiological studies using modern causal inference methodology.

2020

• Helene Charlotte Rytgaard. Targeted causal learning for longitudinal data.